∫ln(1+(√(x^2 +2x+4)))dx


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Question Number 146959 by Gbenga last updated on 16/Jul/21

$\int l n (1 + \sqrt{x^{2} + 2 x + 4}) d x$
	Answered by mindispower last updated on 17/Jul/21
	$⇔∫ln(1+(√(y^2 +3)))dy ⇔yln(1+(√(y^2 +3))))−∫((2y^2 )/(1+(√(y^2 +3))))dy=A−B y=(√3)sh(w) ⇔B=∫((6(√3)sh^2 (w)ch(w))/(1+(√3)ch(w)))dw,e^w =t B⇔∫((p(t))/(q(t)))dt,fraction of polynomil easy to find$
	$\Leftrightarrow \int l n (1 + \sqrt{y^{2} + 3}) d y$ $\Leftrightarrow y l n (1 + \sqrt{y^{2} + 3})) - \int \frac{2 y^{2}}{1 + \sqrt{y^{2} + 3}} d y = A - B$ $y = \sqrt{3} s h (w)$ $\Leftrightarrow B = \int \frac{6 \sqrt{3} {s h}^{2} (w) c h (w)}{1 + \sqrt{3} c h (w)} d w, e^{w} = t$ $B \Leftrightarrow \int \frac{p (t)}{q (t)} d t, f r a c t i o n o f p o l y n o m i l e a s y t o f i n d$
	Commented by Gbenga last updated on 17/Jul/21

	$t h a n k s s i r$
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